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Differentiate the function f(x) = sin (c...

Differentiate the function f(x) = sin `(cos sqrt(x)))` with respect to x,

Text Solution

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`f(x) = sec (tan sqrt(x))`
`therefore f(x)=(d)/(dx)[sec (tansqrt(x))]`
`=sec (tan sqrt(x)). tan (tansqrt(x)).(d)/(dx)(tan sqrt(x))`
`=sec (tansqrt(x)).tan(tansqrt(x)).sec^(2)(sqrt(x)).(d)/(dx)(sqrt(x))`
`=sec(tan sqrt(x)). tan (tansqrt(x)).sec^(2)(sqrt(x)). (1)/(2sqrt(x))`
`=(sec(tansqrt(x)). tan (tansqrt(x))sec^(2)(sqrt(x)))/(2sqrtx)`
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